The dielectric anomaly as the insulator-metal transition is approached from the insulating side

Abstract

The dielectric behaviour of monovalent ‘metallic’ impurities is considered as a function of the impurity concentration N as N approaches the critical concentration N c for the onset of metallic behaviour. The different types of screening, namely (1) metallic (Thomas–Fermi, Lindhard), (2) classical semiconductor (Debye–Huckel), and (3) insulator (Penn–Hubbard, Clausius–Mossotti), are briefly reviewed. For the insulator case the Herzfeld criterion, based on the polarization catastrophe resulting from the Clausius–Mossotti relationship, for distinguishing between insulators and metals is discussed. The available experimental dielectric constant data versus doping for metal–ammonia solutions and n-type Si and Ge are reviewed. The reasons for the striking upward deviation from Clausius–Mossotti behaviour for the Si: As data are explored and various alternative approaches are considered. Several theories of the dielectric enhancement are reviewed and a new continuum model calculation of the donor polarizability enhancement is briefly discussed. The complications of donor randomness, central cell corrections, and other factors are considered. Finally an assessment of the agreement between experimental results and theory is attempted.